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The Cosmological Slingshot Scenario
A Stringy Proposal for Early Time Cosmology:
Germani, NEG, Kehagias, hep-th/0611246 Germani, NEG, Kehagias, arXiv:0706.0023
Germani, Ligouri, arXiv:0706.0025
What do we know about
the universe?
Standard cosmologyIt is nearly
homogeneous It is nearly isotropic
The vacuum energy density is very small
It is expanding It is accelerating
The space is almost flat
The perturbations around homogeneity have a flat (slightly red) spectrum
4d metric
WMAP collaboration
astro-ph/0603449
Standard cosmologyIt is nearly
homogeneous It is nearly isotropic
The vacuum energy density is very small
It is expanding It is accelerating
The space is almost flat
4d metric
Einstein equationsHubble equation
Energy density
Curvature term
The perturbations around homogeneity have a flat (slightly red) spectrum
Standard cosmologyIt is nearly
homogeneous It is nearly isotropic
The vacuum energy density is very small
It is expanding It is accelerating
The space is almost flat
4d metric
Hubble equation
to
a
t
Plank
tPlank
Big
Bang
Solution
The perturbations around homogeneity have a flat (slightly red) spectrum
Standard cosmologyIt is nearly
homogeneous It is nearly isotropic
The vacuum energy density is very small
It is expanding It is accelerating
The space is almost flat
to
ttPlank
The perturbations around homogeneity have a flat (slightly red) spectrum
is constant in the observable region of 1028 cm
Causally disconnected regions are in equilibrium!
Standard cosmologyIt is nearly
homogeneous It is nearly isotropic
The vacuum energy density is very small
It is expanding It is accelerating
The space is almost flat
The perturbations around homogeneity have a flat (slightly red) spectrum
Isotropic solutions form a subset of measure zero on the
set of all Bianchi solutions
Perturbations around isotropy dominate at early time, like a -
6 , giving rise to chaotic behavior!
Belinsky, Khalatnikov, Lifshitz, Adv. Phys. 19, 525 (1970)
Collins, HawkingAstr.Jour.180, (1973)
Standard cosmologyIt is nearly
homogeneous It is nearly isotropic
The vacuum energy density is very small
It is expanding It is accelerating
The space is almost flat
The perturbations around homogeneity have a flat (slightly red) spectrum
It is a growing function
Since it is small today, it was even smaller at earlier time!
(10-8 at Nuc.)
Standard cosmologyIt is nearly
homogeneous It is nearly isotropic
The vacuum energy density is very small
It is expanding It is accelerating
The space is almost flat
The perturbations around homogeneity have a flat (slightly red) spectrum
What created perturbations?
If they were created by primordial quantum fluctuations, its resulting spectrum for normal
matter is not flatTheir existence is necessary for the formation of structure
(clusters, galaxies)
The perturbations around homogeneity have a flat (slightly red) spectrum
The perturbations around homogeneity have a flat (slightly red) spectrum
Plank
tPlank
Big
Bang
Solving to the problemsInflation
Plank
Standard cosmologyIt is nearly
homogeneous It is nearly isotropic
The vacuum energy density is very small
It is expanding It is accelerating
The space is almost flat
tearlier < tNuc
to
a
t
It is nearly homogeneous
The space is almost flat
It is nearly isotropic
Guth, PRD 23, 347 (1981) Linde, PLB 108, 389
(1982)
The perturbations around homogeneity have a flat (slightly red) spectrum
It is nearly isotropic
The space is almost flat
Plank
Bounce
Standard cosmologyIt is nearly
homogeneous
The vacuum energy density is very small
It is expanding It is accelerating
The space is almost flat
tearlier< tNuc
to
a
t
Quantu
m r
egim
e
It is nearly homogeneous
Plank
to
a
t
Bounce
Plank
to
a
t
Inflation
Standard cosmologyIt is nearly
homogeneous It is nearly isotropic
The vacuum energy density is very small
It is expanding It is accelerating
The space is almost flat
The perturbations around homogeneity have a flat (slightly red) spectrum
tearlier< tNuc
Quantu
m r
egim
eC
an t
he b
ounce
be c
lass
ical?
Mirage cosmology
Higher dimensional
bulk4d flat s
lice
3-Bra
ne
Warping factor
Matter
Universe
Cosmological evolution
Plank
to
a
ttearlier
Kehagias, Kiritsishep-th/
9910174
PlankPlank
tPlank
Big
B
ang
Mirage cosmology
to
a
ttearlier
Increasing
warping
Monotonousmotion
Expanding Universe
How can we obtain a bounce?
A minimum in the warping
factorA turning point in the motion
Solve Einstein
equationsSolve
equations of motion
Slingshot cosmology
10d bulk IIB SUGRA solution
4d flat
slice
BPS
Warping factor
D3-Bra
neCosmological
expansion
Plank
to
a
ttearlier
Xaü
x||
Germani, NEG, Kehagias
hep-th/0611246
Slingshot cosmology
Xaü
x||
Plank
to
a
ttearlierXa
ü
Dilaton field Induced metric
RR field
Turning point
Bounce
Burgess, Quevedo, Rabadan, Tasinato, Zavala, hep-th/0310122
6d flat euclidean metric
Warping factor
Slingshot cosmology
Xaü
Plank
to
a
ttearlierXa
ü
Transverse metric
AdS5xS5 space
Free particle
Turning point
Bounce
Non-vanishing impact parameter
Non-vanishing angular momentum
l
Heavy source Stack of branes
Burgess, Martineau , Quevedo, Rabadan, hep-th/0303170 Burgess, NEG, F. Quevedo, Rabadan, hep-th/0310010
Non-vanishing angular momentum
l
6d flat Euclidean metric
Slingshot cosmology
Xaü
Plank
to
a
ttearlierXa
ü
AdS5xS5 space
Free particle
Heavy source Stack of branes
There is no space curvature
Can we solve the flatness problem?
Flatness problemis solved
There is no space curvature
Slingshot cosmologyPlank
to
a
ttearlier
Constraint in parameter
space
Slingshot cosmologyPlank
to
a
ttearlier
What about isotropy?
Dominates at early time, avoiding chaotic behaviour
All the higher orders in r´
Isotropy problem is
solved
Slingshot cosmologyPlank
to
a
ttearlier
And about perturbations?
Induced scalar Bardeen potential
Slingshot cosmologyPlank
to
a
ttearlier
And about perturbations?
Scalar fieldHarmonic oscillator
Growing modes
Oscilating modes
Frozen modes
Decaying modes
Frozen modes survive up to late times Decaying modes do not
survive
Boehm, Steer,hep-th/0206147
Germani, NEG, Kehagias
arXiv:0706.0023
Frozen modes
Slingshot cosmologyPlank
to
a
ttearlier
Power spectrum
= < >
Created by quantum perturbations
h*
r *= kL / lc Creation of the
mode
l = lc Creation of the mode
Slingshot cosmologyPlank
to
a
ttearlier
Power spectrum h*
l > lc Classical mode
l < lc Quantum
mode
Hollands, Waldgr-qc/0205058
l = k /a = kL / rWe get a flat
spectrum
Slingshot cosmologyPlank
to
a
ttearlier
Gravity is ten dimensional
Late time cosmology
Formation of structure
Kepler laws
Real life!
Compactification
AdS throat in a CY space
AdS throat
Top of the CY
Mirage dominate
d era
Local 4d gravity
dominated erabackreaction
Mirage domination in
the throat
Local gravity domination in
the top
The transition is out of our
control
Open Points
The price we paid is an unknown transition region between local and mirage
gravity (reheating)
It is nearly isotropic
The perturbations around homogeneity have a flat
spectrum
The space is almost flat
Slingshot cosmologyIt is nearly
homogeneous
The vacuum energy density is very small
It is expanding It is accelerating
Nice Results
Klevanov-Strassler geometry gives a slightly red spectral index, in agreement with
WMAPProblems with Hollands and Wald proposal are avoided in
the Slingshot scenario
An effective 4D action can be found
There is no effective 4D theory
Back-reaction effects should be studied
Thanks!